Let $G$ be a finite group and let $mathcal{P}=P_{1},ldots,P_{m}$ be a sequence of Sylow $p_{i}$-subgroups of $G$, where $p_{1},ldots,p_{m}$ are the distinct prime divisors of $leftvert Grightvert $. The Sylow multiplicity of $gin G$ in $mathcal{P}$ is the number of distinct factorizations $g=g_{1}cdots g_{m}$ such that $g_{i}in P_{i}$. We review properties of the solvable radical and the solvable residual of $G$ which are formulated in terms of Sylow multiplicities, and discuss some related open questions.